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Number of vertices formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.
3

%I #11 Nov 16 2022 08:53:36

%S 4,8,32,144,468,1160,2512,4836,8468,13760,21784,31168,46596,64760,

%T 86912,114656,154400,194116,253160,310408,382712,469296,580688,677656,

%U 822928,969880,1141112,1319984,1566512,1755032,2080376,2349188,2686452,3052184,3450348,3800756,4387404,4880560,5443192

%N Number of vertices formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.

%H Scott R. Shannon, <a href="/A358408/a358408.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A358408/a358408_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A358408/a358408_2.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A358408/a358408_3.png">Image for n = 10</a>.

%F a(n) = A358409(n) - A358407(n) + 1 by Euler's formula.

%Y Cf. A358407 (regions), A358409 (edges), A355799, A331449.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Nov 14 2022